In a previous paper we have established the theory of transsnite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of innnitary rewriting, the BB ohm model of the lambda calculus can be seen as an innnitary term model. In contrast to term rewriting, there are several diierent possible notions of innnite term, whic...

Undecidability results in rewriting have usually been proved by reduction from undecidable problems of Turing machines or, more recently, from Post’s Correspondence Problem. Another natural candidate for proofs regarding term rewriting is Recursion Theory, a direction we promote in this contribution. We present some undecidability results for “primitive” term rewriting systems, which encode pri...

We consider combinations of term rewriting with built-in operations which compute objects of some external domain from ground terms. Combining a canonical term rewriting system with a computation relation does in general not lead to a canonical simpliication relation. We show how a canonical simpliication system can be constructed for such rewrite systems with built-in operations. Decomposition...

We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left-and right-hand sides of rewrite rules, but introduce the notion of dependency pairs to compare left-hand sides with special subterms of the right-hand sides. This results in a technique which allows to apply existing methods for...